For describing the background of the invention, particular reference is made to the following publications.    [1] Moran P R. A flow velocity zeugmatographic interlace for NMR imaging in humans. Magn. Reson. Imaging 1982; 1:197-203.    [2] Van Dijk P. Direct cardiac NMR imaging of heart wall and blood flow velocity. J. Comput. Assist. Tomogr. 1984; 8:429-436.    [3] Bryant D J, Payne J A, Firmin D N, Longmore D B. Measurement of flow with NMR imaging using a gradient pulse and phase difference technique. J. Comput. Assist. Tomogr. 1984; 8:588-593.    [4] Nayler G L, Firmin D N, Longmore D B. Blood flow imaging by cine MR imaging. J. Comput. Assist. Tomogr. 1986; 10:715-722.    [5] Zhang S, Block K T, Frahm J. MR imaging in real time Advances using radial FLASH. J. Magn. Reson. Imaging. 2010; 31:101-109.    [6] Uecker M, Hohage T, Block K T, Frahm J. Image reconstruction by regularized nonlinear inversion—Joint estimation of coil sensitivities and image content. Magn. Reson. Med. 2008; 60:674-682.    [7] Uecker M, Zhang S, Frahm J. Nonlinear inverse reconstruction for real-time MRI of the human heart using undersampled radial FLASH. Magn. Reson. Med. 2010; 63:1456-1462.    [8] Uecker M, Zhang S, Voit D, Karaus A, Merboldt K D, Frahm J. Real-time MRI at a resolution of 20 ms. NMR Biomed. 2010; 23:986-994. 358.    [9] Zhang S, Uecker M, Voit D, Merboldt K D, Frahm J. Real-time cardiovascular MR at high temporal resolution: Radial. FLASH with nonlinear inverse reconstruction. J. Cardiovasc. Magn. Reson. 2010; 12:39.
Since the conception of MRI in 1973, a major driving force of its further technical, scientific and clinical development is the quest for speed. Historically, it took more than a decade before the fast low-angle shot (FLASH) MRI technique (U.S. Pat. No. 4,707,658 A) reduced the acquisition times for a cross-sectional image to the order of one second and allowed for a continuous imaging due to the generation of a sufficiently strong steady-state MR signal. Nevertheless, the monitoring of dynamic processes in real time remained hampered in particular due to the need for still relatively long measuring times of several hundreds of milliseconds for images with a reasonable spatial resolution. High-speed acquisition techniques have been developed for real-time MRI which suffer from a number of specific drawbacks. For example, so-called single-shot gradient-echo sequences such as echo-planar imaging and spiral imaging are prone to geometric distortions or even local signal losses that are caused by their inherent sensitivity to off-resonance effects, tissue susceptibility differences, and magnetic field inhomogeneities, which are unavoidable in many parts of the body. Complementary, single-shot MRI sequences that employ radiofrequency-refocused spin echoes or stimulated echoes and therefore are free from such problems, lead to a pronounced radiofrequency (RF) power absorption with the risk of local tissue heating or suffer from a compromised signal-to-noise ratio, respectively.
An essential improvement for MRI in real time has been obtained with a combination of FLASH sequences with radial data sampling and view sharing of successive raw data acquisitions (see S. Zhang et al. [5]). The radial data sampling allows for a moderate undersampling factor (about 2) and results in an image raw data acquisition of about 250 ms per frame. With a reconstruction of image updates using current image raw data that corresponds to only a part of a frame together with preceding image raw data (i.e., a so-called ‘sliding window’ method), even a temporal resolution of about 50 ms can be obtained resulting in a video frame rate of 20 MR images per second. However, with the method of S. Zhang et al. [5], disadvantages with regard to the image quality may result from the fact that the total acquisition time per image remains unchanged, that is as long as 250 ms. A further improvement of the imaging process has been obtained by an application of a nonlinear inverse reconstruction method to even more strongly undersampled image raw data of a radial FLASH acquisition (see [6] to [9]).
Furthermore, velocity-encoded phase-contrast MRI is a well established method for dynamically mapping flow velocities which has been developed during the early stages of MRI, e.g. see [1] to [4]. In its most common form velocity-encoded phase-contrast MRI is based on the phase difference between two cross-sectional images acquired with different bipolar velocity-encoding gradients. These velocity-encoding gradients are characterized by a self-compensating waveform and a resulting zero-order gradient moment=0 that leaves stationary spins unaffected but causes a phase for flowing spins corresponding to a first-order gradient moment>0. The zero-order gradient moment is the time integral of the gradient, while the first-order gradient moment is the time integral of the gradient multiplied with the time. For spins that are flowing with a constant velocity, the net phase difference is directly proportional to the velocity. The results of a velocity-encoded phase-contrast MRI measurement may be represented in a 3D dataset which comprises two spatial dimensions and one velocity (phase difference) dimension, so that each image pixel presents with a unique velocity value.